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Abstract

This manuscript is concerned with consistent estimation of the distribution and the density function of waiting time of a cyclic Poisson process with linear trend. It is assumed that the period of the cyclic component is known, but the slope of the linear trend as well as the cyclic component of the intensity function is unknown. The main discussion in this manuscript is the consistency of estimator of the distribution and the density function of waiting time of the process being discussed. In addition, consistent estimation of the slope of the linear trend and the cyclic component of the intensity function are also discussed.